Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | Aut(G) = D4×S5 (order 960) · Inn(G) = C22×A5 · Out(G) = C22 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, cosocle | C2 | C22×A5 |
| commutator, hypocenter | SL(2,𝔽5) | C22 |
| Fitting, hypercenter | D4 | A5 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2 ◁ D4 | |
83 conjugacy classes of subgroups.
| minimal degree | μ(G) = 48 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 48 points:
(1,11,8,21,16)(2,24,6,5,3)(4,10,17,33,27,12,20,7,30,15)(13,35,41,29,14)(18,28)(22,42,46,38,25,31,40,44,36,34)(23,37,39,32,26)(47,48);(1,27,9,4,6,18,5,15,19,12,16,28)(2,25,41,7,26,46,8,34,39,17,14,44)(3,38,21,10,29,30,11,36,24,20,32,33)(13,48,35,22,43,40,23,47,37,31,45,42)24 conjugacy classes — view the full character table.
| maximal subgroup of | #11751520, #11751521, #11751545, … |
| maximal normal subgroup of | #11751520, #11751521, #11751545, … |
| maximal quotient of | #11751534, C22⋊#6732, #11751538, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 957);